# Multiplicity distribution in pseudo-rapidity windows and charge conservation

## TL;DR

This paper models charged particle multiplicity distributions within pseudo-rapidity windows at the LHC, considering charge conservation, and compares two probability models to experimental data from CMS and ALICE.

## Contribution

It introduces a novel analysis of multiplicity distributions using convolution and Glauber-Lachs models under charge conservation constraints.

## Key findings

- Both models fit the data well within the studied windows.
- The double Glauber-Lachs formula effectively describes the global structure.
- Charge conservation impacts the shape of multiplicity distributions.

## Abstract

Charged multiplicity distribution in a pseudo-rapidity window is formulated under the assumption that the charge conservation is satisfied in the full phase space. At first, we analyze measured charged particle multiplicity distributions in pseudo-rapidity windows in LHC by CMS and ALICE collaborations with the two probability distributions. One is the convolution of negative binomial and Poisson distributions, and the other is the Glauber-Lachs formula. Each distribution is considered as an analogy of the quantum optics. Next, we analyze the data with the double GL formulae for $|\eta|<2.4$ at 7 TeV by the CMS collaboration and for $|\eta|<1.5$ at 8 TeV by the ALICE collaboration to describe the global structure of measured distributions.